As a mathematician, Archimedes specially studied circles, spheres and cones, and wrote many mathematical works, such as On Spheres and Cylinders, On Conical Surfaces and Spheres, Quadrature of Parabola, On Spiral, etc. At the same time, he broke through Pythagoras and others' abstract mathematical research methods, and linked mathematical research with practical application, which had a far-reaching impact on later generations.
As an engineer, Archimedes once made a variety of instruments and equipment. The planetarium he made can show the celestial motion very realistically, even the solar eclipse can be vividly shown. The spiral water lift, a household appliance invented by him, is still used in Egypt and other places. He invented the trebuchet for war, which kept the Roman army attacking Syracuse out of the city for three years.
As a mechanic, Archimedes is the founder of statics, and he has written many mechanical works, such as On the Balance of Flat Plate, On Floating Body, On Lever and On Center of Gravity. In On the Balance of Flat Plates, he systematically demonstrated the lever principle. In On Floating Bodies, he demonstrated the law of floating bodies.